Okay, so I bought the call option for XYZ with the strike price at 50 for $2 (or $200). The at-the-money option had a delta of 0.5 and 45 days to expiry. The above diagram shows what my potential P/L would be once it crosses above the breakeven at 52. So far, so good. Now suppose in less than 2 hours, XYZ rises to 55 and I exit the trade at $3 ($100 profit). If going strictly by the textbook example, I shouldn't be making any money before XYZ rises above the breakeven at 52. But this isn't true at all. When the price rises from 50 to 52, the option price also rises accordingly and I can almost always get out with a profit. But my real question is regarding the delta. With a delta of 0.5, I should make $250 when XYZ rises from $50 to $55. But when does the option become "in-the-money", at which point the delta is more close to 1.0? Frankly, I don't. Hence, I have no idea what the option price would be when XYZ is trading at 55. And without this information, how would I know how many contracts to trade?
It had and still has intrinsic time value... The textbook examples are for the expiration date... Regarding the Greeks: they are Greek to me as well... ;-), one can trade options also w/o knowing anything of the Greeks... For me personally it is in the money if my pos is simply in the profit zone... ;-) But the correct interpretation is: it is in the money if the price of the underlying is above the strike of your long call option (or below the strike of your long put option) at any point in time. Regarding delta: it can be that it gets updated only in certain intervalls of the day, or maybe even only at EOD... And: it depends on how one measures volatility, ie. IMHO like the volatility the delta (since it depends on vola) is just an individual interpretation... (but I could be wrong)... Check this: http://www.investopedia.com/university/option-greeks/greeks2.asp
in your example the stock would rally to 51 and you will make 50 cents. however the delta will go up from 50 to 60 and from 51 to 52 you will make 60 cents and the delta will go to 70 so from 52 to 53 you will make 70 cents. the change in delta as spot price moves is called gamma and it can have a huge effect on your pnl. The cost of gamma is theta which is why options have a time value to them. Your pnl is : (delta*change in stock) + 1/2 gamma* (change in stock)^2 - theta botpro doesn't know what he's talking about. Greeks are important to know if you plan to trade options before expiry.
"One interpretation of Delta used by traders is to read the value as a probability number - the chance of the option expiring in-the-money. " Quoted from the above linked site. As said, I wouldn't want to waste my time with the Greeks... It's like TA... Just watch closely the price action of the option (ie. the actual premium in the market), and as well the price action (and direction) of the underlying... And _never_ keep an option until the expiration date! Close it as early as possible. Only exception: when it has no value then let it go, maybe a miracle can happen in the very last minute... Ie. apply the KISS principle...
Sirius I would strongly recommend taking some time to read (and re-read) newwurlmn's response. There are numerous online option pricing calculators that you can use to help bring it to life. If the stock increased to $55 within 2 hours as per your example, the $50 strike call option would be trading for more than $5 as it'll still have time premium. Again, see newwurlmn's p&l drivers